Re-entry trajectory optimization using Radau pseudospectral method

To increase the convergence rate of the numerical method, we employ the Radau pseudospectral method (RPM) in solving the optimal re-entry trajectory for the reusable launch vehicle. In this method, a finite base of global Lagrange interpolating polynomials is used to approximate the states and control at a set of Legendre-Gauss-Radau points. The time derivative of the state in the dynamic equations is approximated by the derivative of the interpolating polynomial, therefore they can be converted to the differential-algebraic equations at the Legendre-Gauss-Radau points. Consequently, the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming (NLP) problem. Then, the resulting NLP problem is solved by a sparse nonlinear programming solver named SNOPT. Finally, simulation results show that the optimized re-entry trajectory satisfies the path constraints and the boundary constraints successfully. The results indicate that the RPM can be applied to fast trajectory-generation problems in practical engineering due to its high efficiency and high precision.